Using the fact that <msqrt> n </msqrt> is an irrational number whenever n is not

Patatiniuh 2022-07-06 Answered
Using the fact that n is an irrational number whenever n is not a perfect square, show 3 3 + 7 + 21 is irrational.
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Answers (2)

cefflid6y
Answered 2022-07-07 Author has 13 answers
If ( 1 + 3 ) ( 1 + 7 ) is rational, then
12 ( 1 + 3 ) ( 1 + 7 ) = 12 ( 1 3 ) ( 1 7 ) ( 2 ) ( 6 ) = 1 3 7 + 21
is also rational.
So, 1 2 [ ( 1 + 3 ) ( 1 + 7 ) + 1 3 7 + 21 ] 1 = 21 is rational.
This leads to a contradiction.
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EnvivyEvoxys6
Answered 2022-07-08 Author has 7 answers
N = 3 + 7 + 21 N 21 = 3 + 7 N 2 + 21 2 N 21 = 10 + 2 21 21 = N 2 + 11 2 + 2 N
So 21 is rational, which is a contradiction.
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